Ratio abstraction over discrete magnitudes by newly hatched domestic chicks (Gallus gallus)

Abstract

A large body of literature shows that non-human animals master a variety of numerical tasks, but studies involving proportional discrimination are sparse and primarily done with mature animals. Here we trained 4-day-old domestic chicks (Gallus gallus) to respond to stimuli depicting multiple examples of the proportion 4:1 when compared with the proportion 2:1. Stimuli were composed of green and red dot arrays; for the rewarded 4:1 proportion, 4 green dots for every red dot (e.g. ratios: 32:8, 12:3, and 44:11). The birds continued to discriminate when presented with new ratios at test (such as 20:5), characterized by new numbers of dots and new spatial configurations (Experiment 1). This indicates that chicks can extract the common proportional value shared by different ratios and apply it to new ones. In Experiment 2, chicks identified a specific proportion (2:1) from either a smaller (4:1) or a larger one (1:1), demonstrating an ability to represent the specific, and not relative, value of a particular proportion. Again, at test, chicks selectively responded to the previously reinforced proportion from new ratios. These findings provide strong evidence for very young animals’ ability to extract, identify, and productively use proportion information across a range of different amounts.

Full text

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Scientific RepoRts | 6:30114 | DOI: 10.1038/srep30114
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Ratio abstraction over discrete
magnitudes by newly hatched
domestic chicks (Gallus gallus)
Rosa Rugani1,*, Koleen McCrink2,*, Maria-Dolores de Hevia3,4, Giorgio Vallortigara5 &
Lucia Regolin1
A large body of literature shows that non-human animals master a variety of numerical tasks, but
studies involving proportional discrimination are sparse and primarily done with mature animals. Here
we trained 4-day-old domestic chicks (Gallus gallus) to respond to stimuli depicting multiple examples
of the proportion 4:1 when compared with the proportion 2:1. Stimuli were composed of green and
red dot arrays; for the rewarded 4:1 proportion, 4 green dots for every red dot (e.g. ratios: 32:8, 12:3,
and 44:11). The birds continued to discriminate when presented with new ratios at test (such as 20:5),
characterized by new numbers of dots and new spatial congurations (Experiment 1). This indicates
that chicks can extract the common proportional value shared by dierent ratios and apply it to new
ones. In Experiment 2, chicks identied a specic proportion (2:1) from either a smaller (4:1) or a larger
one (1:1), demonstrating an ability to represent the specic, and not relative, value of a particular
proportion. Again, at test, chicks selectively responded to the previously reinforced proportion from
new ratios. These ndings provide strong evidence for very young animals’ ability to extract, identify,
and productively use proportion information across a range of dierent amounts.
Humans and non-human animals can solve rudimentary mathematical operations such as ordering, addition and
subtraction over discrete numbers1–7; for a review see ref. 8), but studies involving discrimination of numerical
ratios over discrete amounts are scarce. Some theorists have posited that the representational format of propor-
tional information is comparable to the representation of discrete numbers9–11, which suggests that proportional
reasoning would also be present in those same young animal populations who can represent discrete number.
For this reason, here we use very young domestic chicks as a test case of whether immature organisms can extract
proportional information over discrete sets of objects, without a signicant amount of life experience. If this pro-
portional information is represented in a specic, non-relative, fashion, these naïve newborn chicks will be able
to exibly compare proportions to other proportional magnitudes that are larger or smaller.
Several studies have shown prowess with discrete numerical magnitude in mature birds12–14 as well as newborn
chicks15–18. For example, Emmerton and Renner12 trained pigeons to respond to a particular “anchor” amount,
and found that the birds were able to select this numerical magnitude in the context of multiple comparisons,
and despite changes in surface features such as area or luminance. ese representations are thought to be sup-
ported by an evolutionarily ancient system for representing magnitudes in an analog fashion19,20. ere is also
evidence that mature animals, such as monkeys, are able to go beyond representing single magnitudes, and can
represent proportional relations between two magnitudes11,21,22. Additionally, Rugani et al.20 found that day-old
chicks can represent proportions of two blocks of continuous area20. However, it is unclear whether this same
early-developing propensity would be found for discrete stimuli, over which area statistics must be extracted from
the bounded objects found in the scene. For purposes of foraging, overall area of a stimulus is the most critical
cue to abundance and opportunity, and animals prioritize area when choosing their behavioral response23. us,
chicks may be only able to reason proportionally in an ecologically valid scenario of apparent area discrimination.
If chicks - an animal model that is known to master numerical discrimination, ordinality, and arithmetic calcula-
tions15,16,24,25 - possess a proportional reasoning system that can take as input any type of quantity (either spatial
1Department of General Psychology, University of Padova, Padova, Italy. 2Department of Psychology, Barnard
College, Columbia University, USA. 3Université Paris Descartes, Sorbonne Paris Cité, Paris, France. 4CNRS UMR
8242, Laboratoire Psychologie de la Perception, Paris, France. 5Center for Mind/Brain Sciences, University of Trento,
Rovereto (Trento), Italy. ∗These authors contributed equally to this work. Correspondence and requests for materials
should be addressed to R.R. (email: rosa.rugani@unipd.it)
Received: 22 March 2016
Accepted: 29 June 2016
Published: 28 July 2016
OPEN

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and continuous, or bounded and discrete), then we would expect them to display sensitivity to proportions like
the mature animals studied by Vallentin and Nieder11 and Drucker et al.22.
In the current study, we performed two experiments. In Experiment 1, we replicate and extend Rugani et al.20
by examining whether chicks can selectively respond to, and then generalize from, a particular proportion of
two types of discrete object arrays. In a training session, four-day-old domestic chicks were rewarded with food
aer circumnavigating a panel depicting a target proportion of discrete, bounded objects (4 green dots for every
1 red dot, or 4:1; see Table1), which was presented side-by-side with a neutral, unrewarded, proportion of 2:1.
In a set of subsequent testing trials chicks were presented with new (never seen during training) sets of 2:1 and
4:1 exemplars, and their rst panel circumnavigated was scored. If chicks can represent proportions over discrete
objects and not simply continuous area (see Table2), they will preferentially navigate to the previously rewarded
proportion during testing trials. In Experiment 2 we investigated whether day-old chicks could identify a specic
ratio and discriminate it from a smaller and a larger ratio. Chicks learned to respond to stimuli characterized by a
2:1 proportion, specied by green and red dots (positive stimulus) when compared either with stimuli depicting a
smaller (1:1) or a larger (4:1) proportion (neutral stimuli). As in Experiment 1, we created two sets of stimuli, one
for training and one for test (see Table3), which controlled for absolute overall number or number of each type
of sub-element for each set and for each ratio (see Table4). During training and testing a positive stimulus was
always coupled to a neutral stimulus (4:1 or 1:1). If chicks are able to form an absolute, and not relative, representa-
tion of a particular proportion, they will preferentially navigate to new examples of the previously rewarded target
proportion when paired with new examples of a neutral stimulus that depicts either a larger or smaller proportion.
Results
Chicks can extract a proportional value and productively use it in new contexts. Moreover, they can generalize to
new exemplars and new numbers. Results of both experiments are depicted in Fig.1. On each test trial, we scored
the rst panel circumnavigated by the chicks. We calculated the number of correct trials and the percentages
were computed as: (Number of Correct Choices/20) × 100. In Experiment 1 chicks (n = 10) circumnavigated
the panel depicting the positive stimulus (4:1) at above-chance levels: M = 77.18%, SE = 3.53; one-sample t-tests
against 50% chance value t(9) = 7.71, p < 0.001. In order to assess whether the overall performance depended on
learning, which might have occurred during testing, we considered the rst ve trials of each session. From the
rst trials chicks’ performance was statistically above chance (M = 80.00%, SE = 4.22, one-sample t-tests against
50% chance value t(9) = 7.12, p < 0.001), indicating that they could abstract ratios and generalize them to new
exemplars immediately aer training. In a further analysis we selectively considered the very rst trial, and com-
puted the number of chicks that chose the correct proportion; as a group, chicks signicantly selected the correct
proportion (10/10, binomial sign test p < 0.01).
In Experiment 2, a paired-sample t-test did not reveal any dierence between the neutral stimulus types (4:1 :
M = 70.00, SE = 3.69 and 1:1: M = 68.33, SE = 3.86; t(10) = 0.30; p = 0.77). erefore we merged the two stimuli
types, and found that chicks (n = 12) circumnavigated the panel depicting the positive stimulus (2:1 green:red) at
above-chance levels: M = 69.17%, SE = 2.53, one-sample t-tests against 50% chance value t (11) = 6.98, p < 0.001.
When considering the first five test trials chicks’ performance was statistically above chance (M = 68.33%,
SE = 4.58, one-sample t-tests against 50% chance value t(11) = 4.01, p = 0.002). On the very rst trial, computing
the number of chicks that chose the correct proportion, 9/12 subjects succeeded (binomial test, p = 0.15) (see
Supplementary Information for details on statistical analyses).
Discussion
We investigated the ability of four-day old domestic chicks to extract the proportional relation of two arrays of
discrete objects. In Experiment 1, chicks discriminated between two specic proportions, 4:1 vs. 2:1, in a task
similar to those used to test relative numerical magnitude discrimination. Oen animals are trained to respond
to a target number (e.g. 4) when it is contrasted with another one (e.g. 8), a task that requires discrimination of a
Proportion Neutral Stimuli (2:1) Positive Stimuli (4:1) Total number
of dots in 2:1
vs. 4:1 stimuliColor of dots
Number of
green dots
Number of
red dots
Number of
green dots
Number of
red dots
Training Stimuli
Ratio comparisons
12 6 32 8 18 vs. 40
28 14 12 3 42 vs. 15
20 10 44 11 30 vs. 55
36 18 8 2 54 vs. 10
Mean 24 12 24 6
Testing Stimuli
Ratio comparisons
24 12 56 14 36 vs. 70
4 2 36 9 6 vs. 45
22 11 16 4 33 vs. 20
14 7 20 5 21 vs. 25
Mean 16 8 32 8
Table 1. Experiment 1: Generalization of Trained Ratio.

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smaller stimulus from a larger one. A dierent ability is required to solve a number identication task, in which
a specic number (e.g. 4) must be chosen over a smaller (e.g. 2) or a larger one (e.g. 8). In this case, successful
behavior requires a more abstract identication of an absolute quantity, and not only a smaller vs. larger discrimi-
nation. us, in Experiment 2, we trained chicks to respond to a target proportion (2:1), that was paired in half of
the training trials with a smaller proportion (1:1) and in the other half with a larger one (4:1). Chicks succeeded in
the proportional identication, highlighting their ability to represent the abstracted ratio in an absolute manner.
Again, chicks at test generalized to new ratios, abstracting the positive proportion from new ratios – specied by
discrete numerical magnitudes of red and green dots never seen before – and avoiding multiple dierent types of
irrelevant, neutral ratios. Overall, the present study is the rst to demonstrate that, soon aer birth, animals rep-
resent abstract proportional information from discrete elements and use this information productively in order
to guide adaptive behavior.
ese results are consistent with those found when testing six-month-old infants on their ability to represent
proportions10. Infants were habituated with multiple examples of a certain proportion of yellow and blue dots.
When presented with the same proportion and a new proportion at test, they looked longer at the new one. While
the present study is the rst to show the capability of newborn animals to extract proportionality from discrete
numbers of items, past studies have found that non-human animals can perceive relational quantity in addition
to perceptual features such as overall area. In one such instance, a chimpanzee was able to appreciate fractional
equivalence (1/4, 1/2, 3/4, 1) by matching pictures of three kinds of objects – spherical food items, circular wood
disks and cylindrical water containers – on the basis of their proportional nature26. e animal could match pro-
portions on objects between classes, indicating that this matching went beyond physical resemblances into more
abstract proportional comparison. Adult rhesus monkeys are able to match length proportions (1/4, 2/4, 3/4 and
Proportions
Neutral Stimuli (2:1) Positive Stimuli (4:1)
Number (N) Area (A)
and Perimeter (P) of
green dots
Number (N) Area (A)
and Perimeter (P) of
red dots
Total Number (N) Area
(A) and Perimeter (P)
of dots
Number (N) Area (A)
and Perimeter (P) of
green dots
Number (N) Area (A)
and Perimeter (P) of
red dots
Total Number (N) Area
(A) and Perimeter (P)
of dots
N A P N A P N A P N A P N A P N A P
Training Stimuli
Values (N, A and
P) for each ratio
comparison
12 9.48 37.68 6 4.74 18.84 18 14.22 56.52 32 25.28 100.5 8 6.32 25.12 40 31.6 125.6
28 22.12 87.92 14 11.06 43.96 42 33.18 131.9 12 9.48 37.68 3 2.37 9.42 15 11.85 47.1
20 15.8 62.8 10 7.9 31.4 30 23.7 94.2 44 34.76 138.2 11 8.69 34.54 55 43.45 172.7
36 28.44 113 18 14.22 56.52 54 42.66 169.6 8 6.32 25.12 2 1.58 6.28 10 7.9 31.4
Mean 24 18.96 75.36 12 9.48 37.68 24 18.96 75.36 6 4.74 18.84
Testing Stimuli
Values (N, A and
P) for each ratio
comparison
24 18.96 75.36 12 9.48 37.68 36 28.44 113 56 44.24 175.8 14 11.06 43.96 70 55.3 219.8
4 3.16 12.56 2 1.58 6.28 6 4.74 18.84 36 28.44 113 9 7.11 28.26 45 35.55 141.3
22 17.38 69.08 11 8.69 34.54 33 26.07 103.6 16 12.64 50.24 4 3.16 12.56 20 3.16 12.56
14 11.06 43.96 7 5.53 21.98 21 16.59 65.94 20 15.8 62.8 5 3.95 15.7 25 19.75 78.5
Mean 16 12.64 50.24 8 6.32 25.12 32 100.5 8 6.32 25.12
Table 2. Number of red, green and total dots, and the relative overall area and overall perimeter of each
stimulus used in Experiment 1.
Proportions
Neutral Stimuli (1:1) Positive Stimuli (2:1) Neutral Stimuli (4:1)
Number
of green
dots
Number of
red dots
Total
number
of dots
Number
of green
dots
Number of
red dots
Total
number
of dots
Number
of green
dots
Number of
red dots
Total
number
of dots
Training Stimuli
Ratio comparisons
22 22 44 12 6 18 12 3 15
8 8 16 18 9 27 16 4 20
4 4 8 14 7 21 36 9 45
30 30 60 20 10 30 64 16 80
Mean 16 16 16 8 32 8
Testing Stimuli
Ratio comparisons
36 36 72 8 4 12 24 6 30
12 12 24 28 14 42 12 3 15
7 7 14 20 10 30 52 13 65
41 41 82 40 20 60 8 2 10
Mean 24 24 24 12 24 6
Table 3. Experiment 2: Simultaneous Discrimination of Trained Ratio From Larger and Smaller Ratios.

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4/4) of bars, irrespective of the bars’ absolute lengths11,21. Monkeys can learn to discriminate between two arrays
depicting dierent ratios of positive to negative elements (white squares and black dots), regardless of the absolute
number of elements in the two arrays22.
In a related recent study, domestic chicks preferentially attended to the proportion of dierent-colored areas,
neglecting other information such as the prevalent color or the absolute amount of it20. In the current study, the
chicks were presented with bound, discrete stimuli and not the pixelated continuous area used in Rugani et al.20.
However, it is an open question as to whether the ratios being capitalized upon for the current study were
extracted over numerical magnitudes per se, or spatial extent variables such as area or perimeter (which varied
alongside number in the current design). Even if one was able to perfectly control for the use of spatial extent
within a ratio-specic number design, recent work casts doubt on whether this is a meaningful dissociation in a
proportional context. e representation of one type of ratio (e.g., symbolic, or numeric) evokes the formation of
an abstract proportional relation that transcends both symbolic - non-symbolic format27 and discrete - continu-
ous format28. us, the central value in this set of experiments comes not from an emphasis on number proper as
a cognitive construct, but rather the fact that these very young animals can precociously represent and discrim-
inate proportional information over discrete sets, and do so in a way that suggests the formation of an absolute,
non-relative sense of proportional magnitude akin to that found by Vallentin and Nieder11.
e ability documented here could be advantageous for animals in their natural environment. It is well estab-
lished that the ability to use numerical information, such as “more-than vs. less-than” judgments, constitutes a
survival advantage29. Detecting the dierence between magnitudes, however, is not always sucient to maxi-
mize behavior. In some circumstances numerical discrimination per se is not informative, and adaptive behaviors
require that organisms relate set sizes to each other in the form of proportional comparison. Take, for example,
foraging situations. An important concept when foraging is rate of return: how successful a foraging attempt will
be given the time invested in tandem with the relative yield of one type of desirable food, amongst the number of
Proportions
Neutral Stimuli (1:1) Positive Stimuli (2:1) Neutral Stimuli (4:1)
Number (N) Area
(A) and Perimeter
(P) of green dots
Number (N) Area
(A) and Perimeter
(P) of red dots
Total Number
(N) Area (A) and
Perimeter (P) of
dots
Number (N) Area
(A) and Perimeter
(P) of green dots
Number (N) Area
(A) and Perimeter
(P) of red dots
Total Number
(N) Area (A) and
Perimeter (P) of
dots
Number (N) Area
(A) and Perimeter
(P) of green dots
Number (N) Area
(A) and Perimeter
(P) of red dots
Total Number
(N) Area (A) and
Perimeter (P) of
dots
N A P N A P N A P N A P N A P N A P N A P N A P N A P
Training Stimuli
Values (N,
A and P) for
each ratio
comparison
22 17.38 69.08 22 17.38 69.08 44 34.76 138.2 12 9.48 37.68 6 4.74 18.84 18 14.22 56.52 12 9.48 37.68 3 2.37 9.42 15 11.85 47.1
8 6.32 25.12 8 6.32 25.12 16 12.64 50.24 18 14.22 56.52 9 7.11 28.26 27 21.33 84.78 16 12.64 50.24 4 3.16 12.56 20 15.8 62.8
4 3.16 12.56 4 3.16 12.56 8 6.32 25.12 14 11.06 43.96 7 5.53 21.98 21 16.59 65.94 36 28.44 113 9 7.11 28.26 45 35.55 141.3
30 23.7 94.2 30 23.7 94.2 60 47.4 188.4 20 15.08 62.8 10 7.9 31.4 30 23.7 94.2 64 50.56 201 16 12.64 50.24 80 63.2 251.2
Mean 16 12.64 50.24 16 12.64 50.24 16 12.64 50.24 8 6.32 25.12 32 25.28 100.5 8 6.32 25.12
Testing Stimuli
Values (N,
A and P) for
each ratio
comparison
36 28.44 113 36 28.44 113 72 56.88 226.1 8 6.32 25.12 4 3.16 12.56 12 9.48 37.68 24 18.96 75.36 6 4.74 18.84 30 23.7 94.2
12 9.48 37.68 12 9.48 37.68 24 18.96 75.36 28 22.12 87.92 14 11.06 43.96 42 33.18 131.2 12 9.48 37.68 3 2.37 9.42 15 11.85 47.1
7 5.53 21.98 7 5.53 21.98 14 11.06 43.96 20 15.8 62.8 10 7.9 31.4 30 23.7 94.2 52 41.08 163.3 13 10.27 40.82 65 51.35 204.1
41 32.39 128.7 41 32.39 128.7 82 64.78 257.5 40 31.6 125.6 20 15.08 62.8 60 47.4 188.4 8 6.32 25.12 2 1.58 6.28 10 7.9 31.4
Mean 24 18.96 75.36 24 18.96 75.36 24 18.96 74.36 12 9.48 37.68 24 18.96 74.36 6 4.74 18.84
Table 4. Number of red and green dots and the relative overall area and overall perimeter of each stimulus
used in Experiment 2.
Figure 1. Performance by subjects in both experiments. Error bars indicate +/− one SEM. e dotted line
indicates the chance responding level. Asterisks indicate a signicant dierence from chance, using one-sample
t-tests against. 50 with an alpha level of p < 0.05 (See also Supplementary Information).

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other competitors or undesirable food. is consideration is inherently proportional. In one such example of this,
dierent numbers of pieces of bread thrown at dierent rates were simultaneously oered at opposite sides of a
lake to free-living mallards; these birds divided themselves between resource patches, as if they were simultane-
ously considering the amount of food and the number of animals feeding at the two sites30. is behavior reects
the capability to understand the relative ratios at each site of the available food to the number of competitors in a
naturalistic situation.
Previous comparative studies focusing on numerical understanding have found that the facility to discrimi-
nate between two magnitudes is ratio dependent: as the ratio between the numbers to be discriminated becomes
larger response times decrease and accuracy increases31. is pattern suggests that the responsible cognitive
mechanism is the approximate magnitude estimation system, which allows non-verbal representation of quan-
tities and numerical evaluation8. e similar performance, both qualitatively and quantitatively, in individuals
of dierent species, including human adults when prevented from using language, suggests that this ancient,
non-verbal numerical mechanism is shared across species6. e ratio signature also characterizes some limits
found in proportional reasoning. For instance, six-month old infants can discriminate 2:1 from 4:1, but not
2:1 from 3:110, a limit that is also present in a numerical discrimination task for infants of the same age32,33.
Moreover, monkeys and humans exhibit similar behaviors when discriminating between dierent sets of line
lengths; discrimination in both species is related to the ratio between the two bar lengths, so that as the pro-
portional dierence between the length increases, so does performance11. is suggests that, as for whole num-
bers, the discrimination of proportions depends on the functioning of the approximate magnitude estimation
system11,21, and that organisms possess a sense of absolute proportion in the same way they possess a sense of
absolute magnitude. is accords nicely with the results obtained in Experiment 2, in which the chicks success-
fully went beyond more-than-less-than relative judgments, and were able to select the correct proportion against
both smaller and larger ratios, indicating a sense of absolute and not relative proportion. However, the chicks
took longer to reach training criteria for Experiment 2 (in which they had to choose 2:1 in the context of 4:1 or
1:1, alternately) compared to Experiment 1 (in which they were trained to choose 4:1 in the context of only one
other ratio, 2:1.), 101 trials to 63 trials respectively (see Methods). e formation of this absolute proportion
appeared to be more eortful for the chicks, a phenomenon that could readily be tested using this design in other
non-verbal populations.
Although the ability to represent ratios over discrete items has been found in other non-human animals (such
as rhesus macaques:22), these populations oen have signicant life experience to support this capacity. e pres-
ent study, on the other hand, shows that the ability to discriminate proportional information is precociously
available soon aer birth in non-human animals, just as in humans10. is multi-faceted process should be con-
sidered part of the suite of untrained, early-developing abilities supported by the approximate magnitude system
alongside numerical discrimination, simple arithmetic, and ordinal discrimination. In fact, there is evidence that
this proportional sensitivity may serve as a useful foundation for advanced mathematical skills, even more so than
simple representation and discrimination. Matthews, Lewis, and Hubbard34 recently found that individual dier-
ences in sensitivity to non-symbolic ratios predict formal math performance in adults, and Mohring, Newcombe,
Levine, and Frick35 found that children’s ability to reason about non-symbolic proportions was related to their
understanding of symbolic fractions. By exploring the phylogenetic development of this capacity in special popu-
lations, we can provide unique input to the study of its ontogenetic formation in the human species.
Methods
Subjects. Twenty-two “Hybro” domestic chicks took part in this experiment (Gallus gallus; N = 10 in
Experiment 1, N = 12 in Experiment 2). Chicks were obtained several hours aer hatching, from a local com-
mercial hatchery (Agricola Berica, Montegalda, Vicenza, Italy). On arrival, the chicks were housed individually
in metal cages (28 × 32 × 40 cm). Water and food were available freely. Chicks were oered mealworms (Teneb ri o
molitor larvae) twice a day, to familiarize them with this reinforcement food. Two hours before training the food
was removed from the cages. At the end of training chicks were placed back in their home cages and, two hours
later, they underwent testing individually.
Apparatus. e experimental apparatus for both experiments consisted of a triangular arena (width 60 cm,
height 20 cm) made of uniformly white plastic panels and ooring (see Fig.2). A ‘starting’ area was positioned
10 cm from one vertex of the arena. is was delimited by a transparent removable partition (10 cm × 20 cm). e
transparent partition was used to conne subjects for ve seconds before the beginning of each trial, in order to
give them the possibility of seeing the inner apparatus and the stimuli. During training and testing, two identical
white plastic panels (16.0 × 8.0 cm) were inside the arena. ese were located symmetrically with respect to the
starting area, spaced 6.0 cm apart and located 30.0 cm away from the transparent partition. Panels were provided
with 3.0 cm sides bent back to prevent chicks from looking behind the panel where the mealworm reinforce-
ment was hidden. During the inter-trial period chicks were moved in a separate box (20 cm × 40 cm × 40 cm) for
approximately 30 seconds, to prevent them from seeing the experimenter changing the test stimuli.
Stimuli. For both experiments, the stimuli were composed of green and red dots designed to appear
three-dimensional, generated in Adobe Ilustrator. e diameter of each dot was 0.5 cm. In Experiment 1, the
mean number of overall dots during training for the positive stimuli was 30 (24 green and 6 red) and for the
neutral stimuli 36 (24 green and 12 red). To ensure that chicks were not responding to the overall number of dots
during test, or the mean number of dots for each subelement, the test values were chosen to be psychologically
equidistant from those values rewarded in training, with a mean of 8 red dots for both the neutral and positive
stimuli (a Weber ratio of 1.33, 8 testing : 6 training) and a mean of 16 and 32 green dots for the neutral and pos-
itive stimuli (similar Weber ratios of 1.5 and 1.33, respectively). e mean overall number of dots during testing

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was 24 and 40 for the neutral and positive stimuli (similar Weber ratios of 1.25 and 1.33 compared to overall
number of dots rewarded during training).
In Experiment 2, the mean number of overall dots rewarded in training for the positive stimuli was 24, and
the mean numbers of overall dots for the neutral stimuli sets were 48 for the 1:1 stimuli, 30 for the 4:1 stimuli,
and 36 for the 2:1 positive stimuli (Weber ratios of 2:1, 1.25, and 1.5). Note that if chicks are going to the overall
number of dots, they should approach one of the neutral sets (the 4:1 stimuli) more oen and the other neutral
set (1:1) less oen, in eect cancelling each other out. For the subelements, chicks during training on the positive
stimuli were shown on average 16 green dots and 8 red dots. At the neutral 1:1 test, chicks saw an average of 24
green and 24 red dots; at the positive 2:1 test, chicks saw an average of 24 green dots and 12 red dots; at the neutral
4:1 test chicks saw an average of 24 green dots and 6 red dots. For the red dots, this yields Weber discrimination
values of 3.0, 1.5, and 1.3. Again, note that if chicks are merely choosing a subelement average that is closest to
that trained, the two neutral ratios provide conicting information as to success of this strategy. For the green
dots, this yields identical Weber ratio discrimination values of 1.5 for all stimuli types (1:1, 2:1, and 4:1). To avoid
any congurational learning, for each exemplar ratio (e.g., 32:8) we created ve dierent spatial congurations of
the dots, yielding 20 pairs total of stimuli.
Training. Training occurred in the morning of the fourth day. e two panels were in place, with a meal-
worm located between the starting area and the panel depicting the positive stimulus. e chick was at rst
placed within the arena, in the starting area, for two minutes, free to move around and to get acquainted with
the novel environment (no partition was used to conne the bird in this experimental phase). Five mealworms
were subsequently oered to the subject, whilst in the arena, to get it used to feeding in this new environment.
Following this acclimation period, the subject underwent the training procedure. Initially a piece of mealworm
was positioned in view in front of the panel depicting the positive proportion. ereaer, the food reinforcement
was progressively moved behind the panel depicting the positive ratio, requiring the bird to go behind the panel to
retrieve it. For both the training and the testing trials, the chick was placed for approximately 30 seconds between
trials in an opaque plastic container located outside of the arena while the experimenter changed the stimuli. e
experimenter was located in a laterally neutral location behind the chick – opposite the chick’s line of sight to the
panels - throughout the trials to prevent social cueing. e end of the trial was the rst circumnavigation of one
of the test panels, as determined by the experimenter.
In all correct training trials chicks received reinforcement. To avoid any spatial learning during training, and
also during testing, we changed the le–right (L–R) position of the stimulus associated with food/side of pres-
entation of the positive stimulus, following a semi-random sequence (e.g. L–R–L–R–L–L–R–R–L–R–L–R–L–R–
L–L–R–R–L–R36,37. Learning criterion was set at 16/20 trials correct. e training procedure was identical for
Experiments 1 and 2. e mean number of trials to reach the learning criterion was 63.10 ± 7.64 in Experiment 1
and 101.25 ± 16.39 in Experiment 2.
Test. Two hours aer the end of training each chick underwent the test, which consisted of 20 trials. At the
beginning of each trial, the chick was conned to the starting area, behind the transparent partition, from where
it could see the two panels. e stimuli were located on the front part of each panel (facing the starting area). In
each trial, a pair of test stimuli was used and the le–right position of the positive stimulus was changed from trial
to trial according to the semi-random sequence described above. e chick remained conned in the starting area
for 5 seconds; aerwards, the transparent partition was removed and the chick was free to move. When the chick
had placed its head and about ¾ of its body behind a panel it was deemed to have made a choice, at which point
the trial was considered to be over (only the rst panel chosen was taken into consideration). If the rst panel
Figure 2. e apparatus used in Experiments 1 and 2. Both panels were present in the apparatus during the
training and testing sessions.

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Scientific RepoRts | 6:30114 | DOI: 10.1038/srep30114
approached corresponded to the one depicting the proportion associated at training with food the response was
considered as ‘correct’, otherwise it was considered ‘incorrect’.
e chicks’ behavior was observed from a monitor connected to a video camera so as not to disturb the chicks
by direct observation. All trials were video-recorded. e chicks’ performance was scored o-line by a coder naïve
to the hypotheses of the study. We calculated the number of correct trials and the percentages were computed as:
(Number of Correct Choices/20) × 100. To ensure no item eects were inuencing the results, the training and
testing sets were switched for half the chicks.
In Experiment 1, testing consisted in 20 consecutive trials. In each trial a new pair of stimuli of the new set was
used. During testing the food reinforcement was available behind the panel depicting the positive ratio only in
some pre-established trials (trial numbers 4, 5, 7, 10, 13, 14, 16 and 1920), and chicks could gain the food only by
choosing correctly in those trials. All other trials were unrewarded.
In Experiment 2, to better control for any eect of learning during testing, we changed the testing procedure.
e test phase consisted of two testing sessions, each of which was composed of 30 trials: 20 training trials (tr) and
10 testing trials (T) mixed together (tr, tr, T, tr, tr, tr, T, tr, T, tr, tr, T, tr, tr, T, tr, tr, tr, T, tr, tr, T, tr, T, tr, T, tr, tr, tr,
T). In training trials we used the set of stimuli used at training, and chicks, giving a correct response, received the
reward. In testing trials we used the second set of stimuli and chicks never received the reward.
Ethics Statement. e experiments complied with all applicable national and European laws concerning
the use of animals in research and were approved by the Italian Ministry of Health (permit number: 32662 emit-
ted on 10/1/2012).
All procedures employed in the experiments included in this study were examined and approved by the Ethical
Committee of the University of Padua (Comitato Etico di Ateneo per la Sperimentazione Animale –C.E.A.S.A.) as
well as by the Italian National Institute of Health (N.I.H).
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Acknowledgements
is study was supported by the University of Padova (“Progetto Giovani” 2010, to R.R., prot.: GRIC101142 and
“Progetto di Ateneo” 2012 to R.L. prot. CPDA127200) and by an ERC Advanced Grant (PREMESOR ERC-2011-
ADG_20110406) to G.V., and by R15HD065629-01 from the Eunice Kennedy Shriver National Institute of Child
Health and Human Development to K.M.
Author Contributions
R.R. and K.M. developed the study concept and designed the study. R.R. and L.R. supervised testing and data
collection. R.R. performed the data analysis. R.R. and K.M. interpreted the results under the supervision of L.R.,
G.V. and M.D. R.R., M.D. and K.M. wrote the manuscript, L.R. and G.V. provided critical revisions. All authors
approved the nal version of the manuscript for submission.
Additional Information
Supplementary information accompanies this paper at http://www.nature.com/srep
Competing nancial interests: e authors declare no competing nancial interests.
How to cite this article: Rugani, R. et al. Ratio abstraction over discrete magnitudes by newly hatched domestic
chicks (Gallus gallus). Sci. Rep. 6, 30114; doi: 10.1038/srep30114 (2016).
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